This invention relates to techniques for mapping a stream of information bits sent over a channel in a plurality of signaling slots to the points of an eight dimensional (8D) signal constellation. This invention more particularly relates to mapping techniques for defining the points of an 8D constellation through the use of twenty-nine bits.
An eight-dimensional, sixty-four state convolutionally coded communication system for transmitting information is disclosed in U.S. Pat. No. 4,713,817 to Wei which is hereby incorporated by reference herein. With such a system, Wei teaches how to construct a 19.2 Kbit/second modem which utilizes four 2D constellations, each having one hundred sixty points. Although Wei claims an eight dimensional constellation which is comprised of a concatenation of the four 160 points 2D constellations (e.g. a constellation having 160.sup.4 points), Wei teaches (at Col. 17, lines 57-65) that 536,870,912 points of the 655,360,000 8D points are chosen, and that twenty-nine bits are used to represent those 536,870,912 points. In particular, in accord with the teachings of U.S. Pat. No. 4,597,090 to Forney, Jr., Wei teaches that each of the four 2D constellations should be divided into a group of inner points, and a group of outer points, each outer point being further from the origin than each of the inner points. In the one hundred sixty point 2D constellation, Wei provides one hundred twenty-eight inner points, and thirty-two outer points. Wei then teaches that the 536,870,912 8D points chosen should include only those 8D points having four inner points or three inner points and one outer point distributed over the four 2D constellations.
In representing the 536,870,912 8D points with twenty-nine bits, Wei effectively divides each group of one hundred twenty-eight inner 2D points into four rotational subgroups of thirty-two points each, and each group of thirty-two outer 2D points into four rotational subgroups of eight point each. In choosing (mapping) a point, Wei first uses one bit to indicate whether 8D point has all inner points, or three inner points and one outer point. If the 8D point has all inner points, eight additional bits, two for each 2D constellation, are used to indicate in which of the four rotational subgroups the chosen point is located. The remaining twenty bits (five per 2D constellation) are used to identify the particular point out of the thirty-two points of the rotational subgroup for each 2D constellation. Where the 8D point has an outer point as identified by a first bit, eight additional bits are still used to identify the rotational subgroups. For the inner points, five bits per 2D constellation (total of fifteen) are still utilized to identify the points. However, of the remaining five bits, two bits are used to identify from which of the four 2D constellations the outer point is being chosen, and three bits are used to identify which of the eight outer points of an outer rotational subgroup is being sent.
While the Wei patent as disclosed (as opposed to claimed) is effective in providing a 19.2 Kbit/sec modem, the mapping technique utilized is not necessarily optimal or desirable. In particular, the division of each constellation into inner and outer points does not guarantee or approach an optimal signal to noise ratio, as there exist points among those 536,870,912 8D points chosen which have higher energy than some 8D points which would have had two inner and two outer points.